
Look, I realize I'm not the first person in history to tackle this idea (Simmons' thoughts on this are actually pretty good, by the way). But I've given it some thought, and feel that my list of criteria is a pretty valuable one.
So here goes:
1) The original film must feel dated, bad, or otherwise unsatisfactory in the present day.
This is by far the most important criteria. Indeed, it so important that if a project violates it, no amount of other justifications can save it. There would be a riot if someone suggested remaking The Godfather or Citizen Kane today, because time and fashion haven't reduced their watchability at all. The essentially point is this: for a remake to succeed, there has to be a rationale for why the original can be improved upon. Both Videodrome and Robocop as remakes are irredeemably bad ideas right from the outset because it's not obvious how a modern-day production would be automatically improved.
I just watched Robocop the other day. It's still awesome. The special effects hold up, the pace is snappy and the writing retains the full force of its wit. The one glaring flaw is that Kurtwood Smith gives an acceptable performance as the villain, but it's impossible not to imagine later-Verhoeven heavy Michael Ironside doing an even better job in the role. But on the whole, the film is both endlessly entertaining and surprisingly deep.
Videodrome doesn't just hold up, it's arguably improved by the passing of time. Not only do all the elements hold up (Rick Baker's makeup effects look somewhat out-of-fashion, since they'd almost certainly be done with CGI today, but not bad), but the whole film has this sort of "retro future technology" feel with its heavy emphasis on analog video equipment and videotapes.
Look, this doesn't mean they're perfect movies, or don't have flaws that could be improved in a new version. But a remake implies that these flaws would be corrected merely by a modern-day production of average quality. Bad or dated special effects are an obvious area in which just being a contemporary production implies an improvement.
2) The film must have lasting cultural resonance

Don't remake a movie no one has ever heard of. This is pretty self explanatory. Why re-do an existing property, when you can just go out on your own? Whatever money John Singleton spent acquiring the rights to the forgotten Sons of Katie Elder so he could remake it as the equally forgotten Four Brothers was wasted (come to think of it, any money spent on that movie was wasted. But I digress).
Robocop passes this test easily. Twenty-odd years later, he's still a recognizable character, even for those too young to remember his heyday (myself included).
Videodrome is definitely not. It's most lasting cultural impact has been dialogue being sampled in Industrial music. In fact, the only people who know what Videodrome is (movie nerds) are the people most likely to be pissed off that it's being remade.
3) The film must have a premise that is appealing enough to justify a remake on its own.
When you remake a film, you are basically jettisoning everything besides the premise. So if the first film succeeded because it had great stars, or because of its snappy dialogue, or great art direction, or whatever, remember that this will not necessarily be around for the second version. So if Robocop was so cool because of its combination of violence, humor and satire, and not because the premise "robot cop fights criminals" is can't miss, don't remake it. If Videodrome didn't have James Woods at his best, a super-hot Debbie Harry and David Cronenberg's body-horror weirdness, its premise (I'm not going to attempt a logline-type summary for this one: it's too weird) it would not be remembered today.
4) The film should have a contemporary relevance or hook that is not present in the original, or is heightened from the original
Why would Robocop work better today than it did in the late-Reagan-era crime boom, a time when a future in which crime rates continued to increase at 20% a year on into infinity seemed plausible? It wouldn't. (The original's vision of a ruined hellhole where Detroit once was looks unfortunately accurate, but its portrayal of future Detroit as continuing home of American industry, not so much)
Videodrome actually raises some interesting possibilities, and this is probably how this project got going in the first place. Certainly, the intersection between mass media, violence and the loss of identity is more potent in the internet era. Knowing Hollywood, however, I assume it's just going to be a lot of Web 2.0 crap ("Max Renn has confirmed your friend request!")
***

So these two, obviously, fail. What's a film, off the top of my head, that actually works as a remake? Well, let's look at another Paul Verhoeven action pic: Total Recall.
Now, don't get me wrong. Total Recall is not a bad movie. In fact, it's good. I just watched it the other night and it was totally entertaining.
But that doesn't mean a remake couldn't be worthwhile. Let's look at the criteria.
1) (recall that this one is mandatory) Total Recall has one huge flaw that keeps it from being enjoyable today: Arnold Schwarzenegger. Okay, that's not right actually. Let me rephrase. Total Recall has one huge flaw that keeps it from being unironically enjoyable today. Watching Arnold in one of his least appropriate roles ever (his character is supposed to be an average guy. No one comments on his absurdly muscle-bound appearence. And it goes without saying that no one comments on his thick Austrian accent, even though everyone else in the film speaks with an American accent. Even Martians). The film plays a lot like a live-action comic book as it is, but putting Arnold in there really pushes a lot of scenes over the top in ridiculousness.
2) For a hit when it was originally released, Total Recall is slowly being forgotten. However, it's still recent enough (18 years or so) that there's definitely a demographic that will remember it fondly. And a few rotations on the basic-cable circuit (which it inexplicably doesn't play all the time on) will get the others up to date. Plus, so many other Phillip K. Dick adaptations are considered classics, adding Total Recall back into that canon gives it a hook that lets people who never saw the original a reason to get excited. "Oh, another movie from the same author who wrote Blade Runner? Cool."
3) This is where Total Recall really shines. The very best thing about the film is the heady sci-fi premise. Basically, Arnold's character goes in for a "memory implant vacation," where he will have the memories of a perfect vacation to Mars implanted into his mind without the messy business of actually having to go on the trip. He chooses a special option, a secret agent storyline. But he wakes up during the implantation, finds out that he actually is a secret agent who's memory has been erased, and must go to Mars to stop an evil conspiracy. But is this just the malfunctioning vacation implant? Whether what we're seeing is inside Arnold's mind or actually happening is a constant question throughout the film, and a surprisingly effective mindfuck.
The premise pays off in probably the film's best scene, (Youtube is annoyingly not letting me embed this clip) in which a representative of Rekall, the memory-implant company, tries to talk Arnold back into reality. Without Arnold's cooperation, he will never wake up and will be lobotomized. Or is this representative really working for the evil Cohagen, and simply lying in order to drug and capture Arnold? It's hard to imagine a higher-stakes decision than that--if you're wrong, you're dead. And he only has to be right about something we all take for granted. That we as the audience can't figure it out either is a testament to how well the filmmakers walk the line between the two possibilities. A premise that leads to scenes like the one linked above is a strong premise.
4) It's pretty easy to imagine how to make Total Recall have some sort of contemporary relevance. Great power exerts a hegemonic stranglehold over an oppressed population in order to gouge profits on valuable resource extraction? Sounds like you could adapt that part of the premise to say, the occupation of Iraq, no? The original had a lot of implicit social critique (though not nearly as much as Verhoeven's Robocop or Starship Troopers) and there's plenty of room for the same in a remake.
There's a lot of well-loved Phillip K. Dick adaptations floating around. From the classic Blade Runner to recent hit Minority Report, these mindfuck sci-fi premises work, and Total Recall could work as a much more dramatic and serious film if remade. As it happens, it was recently announced that a producer is in final talks to buy the rights to remake Total Recall. The nerds on the interest will, as a knee-jerk reaction, gnash their teeth and complain. But unlike so many recent remake announcements, this is one that could work.